{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=\"right\" style=\"text-align: right\"><i>Peter Norvig<br>August 2021</i></div>\n",
    "\n",
    "# RaceTrack\n",
    "\n",
    "From 538's [The Riddler](https://fivethirtyeight.com/features/can-you-zoom-around-the-race-track/) on 6 August 2021 (slightly edited):\n",
    "\n",
    "> The game of [RaceTrack](https://link.springer.com/chapter/10.1007/978-3-642-13122-6_26) was published by recreational mathematician [Martin Gardner](http://www.martin-gardner.org/) in [1973](https://www.scientificamerican.com/article/mathematical-games-1973-01/). There have been some neat [digital versions](https://harmmade.com/vectorracer/#) since then, and it’s high time we had a race here: the Riddler-opolis 500!\n",
    ">\n",
    "> You begin at the blue point on the starting line below the circle (diagram shown below) with a velocity vector of zero, and your goal is to circumnavigate the track in a counterclockwise loop. You’ll be moving in straight line segments from point to point on the grid, without ever crashing into the outer wall or the central circle.  (Moving tangent to the circle is allowed, as is being on a grid point along a wall.)\n",
    ">\n",
    "> For each move you have a choice of nine possible destinations, corresponding to the 3x3 grid that surrounds the point formed by adding your current velocity vector to your current position. That is, you can maintain your current velocity, or you can alter your velocity (and hence your destination) by accelerating one grid point in any direction (horizontally, vertically or diagonally). For example, if your first move was up and to the right, then your nine possible second moves are shown below, although two of them will cause you to crash into the central circle and one of them is standing still.\n",
    ">\n",
    "> How quickly can you navigate the track? \n",
    ">\n",
    "> ![](https://fivethirtyeight.com/wp-content/uploads/2021/08/Screen-Shot-2021-08-04-at-10.44.11-PM.png?w=200)\n",
    "\n",
    "\n",
    "# Defining Points, Vectors, and Paths\n",
    "\n",
    "We will need to represent 2-D points on a grid, as well as 2-D vectors for velocity and acceleration. I will use the following choices:\n",
    "- `Point(x, y)`: a point in the 2-D plane, implemented as a complex number.\n",
    "- `Vector(x, y)`: a 2-D vector, also implemented as a complex number.\n",
    "- `Path`: the car's history of position points as it moves, implemented as a list of Points.\n",
    "- `X(point)`, `Y(point)`: the x- and y-coordinates of a point, respectively.\n",
    "- `zero`, `up`, `right`: vectors that stay still, move one unit up, and move one to the right, respectively.\n",
    "- `accelerations`: the nine possible acceleration vectors (to change the car's velocity)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from typing import List, Tuple, Dict, Set\n",
    "\n",
    "Point  = complex\n",
    "Vector = complex\n",
    "Path   = List[Point]\n",
    "\n",
    "def X(point) -> float: \"x-coordinate\"; return point.real\n",
    "def Y(point) -> float: \"y-coordinate\"; return point.imag\n",
    "\n",
    "zero, up, right = Vector(0, 0), Vector(0, 1), Vector(1, 0)\n",
    "\n",
    "accelerations = [up-right,  up,   up+right, \n",
    "                 -right,    zero, right, \n",
    "                 -up-right, -up,  -up+right]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Note:* I debated whether the elements of a `Path` should be just points, or (point, velocity) pairs, because that's what uniquely identifies the state of a car. I decided it was simpler to just use points. Given a path, the velocity can be easily computed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def velocity(path) -> Vector:\n",
    "    \"\"\"Velocity of the car when it is at the end of the path.\"\"\"\n",
    "    return zero if len(path) == 1 else path[-1] - path[-2]  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Defining the Track\n",
    "\n",
    "I want to solve RaceTrack games both on the particular track posed by The Riddler, and on differently-shaped race tracks. I'll define the class `Track` to be a set of points, but annotated with \n",
    "attribute/value pairs (which can vary for different tracks)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Track(Set):\n",
    "    \"\"\"The set of legal points on the track, with any attributes.\"\"\"\n",
    "    def __init__(self, items, **kwds):\n",
    "        self.update(items)\n",
    "        self.__dict__.update(kwds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For The Riddler's track, the track points are all those points on a 15x15 square except the ones that fall inside the circle's radius.  The track also has three attributes:\n",
    "- `track.start`: the single starting point.\n",
    "- `track.finish`: the two endpoints of the finish line.\n",
    "- `track.radius`: the radius of the central circle (whose center, without loss of generality, is the origin)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "side   = range(-7, 8)\n",
    "points = {Point(x, y) for x in side for y in side if abs(Point(x, y)) >= 3}\n",
    "track  = Track(points, start=Point(0, -5), finish=[Point(0, -3), Point(0, -7)], radius=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization\n",
    "\n",
    "It will be really helpful to be able to visualize paths on the track:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(paths=(), track=track):\n",
    "    \"\"\"Plot the track and any paths, along with the start and finish line.\"\"\"\n",
    "    fig, ax = plt.subplots()\n",
    "    plt.xticks([]); plt.yticks([])\n",
    "    ax.set_aspect('equal')\n",
    "    ax.add_artist(plt.Circle((0, 0), track.radius, alpha=1/3, color='k', ec='w'))\n",
    "    ax.plot(*XY(track), 'k,' )                # grid points\n",
    "    ax.plot(*XY([track.start]), 'ks', ms=10)  # start point\n",
    "    ax.plot(*XY(track.finish), 'k-')          # finish line\n",
    "    for path in paths:                        # paths\n",
    "        ax.plot(*XY(path), 'o-')  \n",
    "    plt.title(f'{len(paths)} paths of {set(len(path) - 1 for path in paths)} moves')\n",
    "    \n",
    "def XY(points) -> Tuple[List[float], List[float]]: \n",
    "    \"\"\"A tuple of: (the x-coordinates of points, the y-coordinates of points).\"\"\"\n",
    "    # This converts points into the format that plt.plot expects \n",
    "    return [X(p) for p in points], [Y(p) for p in points]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below is my recreation of The Riddler's diagram of the first two moves. Here and throughout I'll use the convention:\n",
    "- `p` is a point indicating a move.\n",
    "- `v` is the velocity of the move.\n",
    "- `p1` is where the next point would be if the velocity remains constant.\n",
    "- `p2` is where the next point actually is with acceleration applied to change the velocity.\n",
    "\n",
    "In this example, `p` is up and right from the start, and from there there are 9 possible values for `p2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v   = up + right\n",
    "p   = track.start + v\n",
    "p1  = p + v\n",
    "p2s = [p1 + a for a in accelerations]\n",
    "\n",
    "plot([[track.start, p, p2] for p2 in p2s])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Circumnavigating the Track\n",
    "\n",
    "What exactly does it mean to  mean to \"circumnavigate the track in a counterclockwise loop\"? I'll define a circumnavigation (and thus, a *solution*) as a path goes from the plane's fourth [**quadrant**](https://mathworld.wolfram.com/Quadrant.html)  to the first, second, third, and back to the fourth. (Points with an x-coordinate of exactly 0 are considered to be in the first or fourth quadrant.) \n",
    "\n",
    "<center><div><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Cartesian-coordinate-system-with-quadrant.svg/242px-Cartesian-coordinate-system-with-quadrant.svg.png\" width=120></div></center>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_solution(path, goals=(4, 1, 2, 3, 4)) -> bool:\n",
    "    \"\"\"Does the path go through all the goal quadrants in the prescribed order?\"\"\"\n",
    "    i = 0 # Index of next goal to be achieved\n",
    "    for p in path:\n",
    "        if quadrant(p) == goals[i]:\n",
    "            i += 1 # Start looking for the next goal\n",
    "            if i == len(goals):\n",
    "                return True\n",
    "    return False\n",
    "\n",
    "def quadrant(p: Point) -> int: \n",
    "    \"\"\"What quadrant of the 2-D plane is this point in?\"\"\"\n",
    "    if X(p) >= 0:\n",
    "        return 1 if Y(p) > 0 else 4\n",
    "    else: \n",
    "        return 2 if Y(p) > 0 else 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generalize this to other race tracks, you could change the definition of `quadrant` (there could be more than 4 \"quadrants,\" and they could have any shape), and change the `goals` in `is_solution`.\n",
    "\n",
    "# Legal Moves\n",
    "\n",
    "As stated earlier, I want to solve the specific Riddler track, and also make the code general enough that it can handle other tracks. I'll do that by splitting up responsibility for determining legal moves:\n",
    "- `all_moves(path, track)` is general; it returns track points that can be reached with any acceleration.\n",
    "- `riddler_track_moves(path, track)` is specific; it limits moves in the following ways:\n",
    "  - It won't make moves that stay in one place (they are legal, but wasteful on this track).\n",
    "  - It won't pass from the fourth quadrant backwards over the finish line into the third (legal, but wasteful).\n",
    "  - It won't let a move's line segment intersect the central circle (even if the start and end points of the move are on valid track points outside of the circle).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def all_moves(path, track=track) -> Set[Point]:\n",
    "    \"\"\"Moves with any allowable acceleration that end up on the track.\"\"\"\n",
    "    p1 = path[-1] + velocity(path)\n",
    "    return {(p1 + a) for a in accelerations} & track\n",
    "                \n",
    "def riddler_track_moves(path, track=track) -> Set[Point]:\n",
    "    \"\"\"Reasonable moves on The Riddler's track.\"\"\"\n",
    "    p = path[-1]\n",
    "    return {p2 for p2 in all_moves(path, track)\n",
    "            if p2 != p\n",
    "            and not (quadrant(p) == 4 and quadrant(p2) == 3) # Don't go backwards\n",
    "            and not intersects_circle(p, p2, track)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The math for solving for the intersection of a line segment and a circle  [looks complicated](https://stackoverflow.com/questions/6091728/line-segment-circle-intersection), so instead I just define N+1 points along the line from point *p* to point *p2* and check if any of those points is within the radius of the circle. I chose N to be big enough that I believe this approach won't miss any intersection points on our small track."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def intersects_circle(p: Point, p2: Point, track=track) -> bool:\n",
    "    \"\"\"Does any point w on the line from p to p2 fall within radius of center?\"\"\"\n",
    "    return any(abs(w) < track.radius for w in waypoints(p, p2))\n",
    "\n",
    "def waypoints(p, p2, N=20) -> List[Point]:\n",
    "    \"\"\"All the points that are i/N of the way from p to p2\"\"\"\n",
    "    return [p + (i / N) * (p2 - p)\n",
    "            for i in range(N + 1)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Frontier of Possible Paths\n",
    "\n",
    "Now I want to expand paths by adding legal moves to the end until I find solution(s). I could keep *all* my paths in a `list`, but there will be an exponential number of them: O(9<sup><i>n<i/></sup>) paths of length *n*. \n",
    "\n",
    "I am not looking for all solutions, just one fastest solution (or possibly a small sampling of them). So I am willing to discard some partial paths if I can prove that they can never lead to a faster solution than another partial path.\n",
    "    \n",
    "The key idea is that there may be many partial paths that arrive at the some endpoint with the same velocity in the same number of moves. I only need to keep one of them, because they can all be continued in exactly the same ways.\n",
    "\n",
    "I will define a data structure that I call a `Frontier`, which is a dict of `{(endpoint, velocity): path}`. By the nature of dicts, this keeps only one path for each `(endpoint, velocity)` pair. \n",
    "    \n",
    "Here's how I expand a frontier, adding one more move in all possible ways, and discarding duplicates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Frontier = Dict[Tuple[Point, Vector], Path]\n",
    "\n",
    "def expand(frontier, legal_moves=riddler_track_moves, track=track) -> Frontier:\n",
    "    \"\"\"The {(endpoint, velocity): path} frontier extended one move in all legal ways.\"\"\"\n",
    "    return {(p, velocity([path[-1], p])): path + [p] \n",
    "            for path in frontier.values() \n",
    "            for p in legal_moves(path, track)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Note:* Before I added the limitation that moves can't pass backwards from the fourth quadrant to the third, it was possible that two different paths would arrive at the same point in the third quadrant with the same velocity. If  the path that was discarded had circumnavigated and the path that was kept  had not, that was **a bug** that  discarded some valid solutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Searching for the Fastest Solutions\n",
    "\n",
    "Now all I have to do to solve the problem is repeatedly expand the frontier until one or more solutions are found. The first solutions found are guaranteed to be the fastest (i.e., they are the paths with the fewest possible moves), because we are expanding paths one move at a time. In the end, `search` returns a list of all the solutions in the frontier, but there may be many other paths that are not returned, because the frontier only keeps one path for each `(endpoint, velocity)` pair, and there are only so many ways to cross the finish line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def search(track=track, path=None, legal_moves=riddler_track_moves) -> List[Path]:\n",
    "    \"\"\"Find the shortest possible solution paths.\"\"\"\n",
    "    if path is None: path = [track.start]\n",
    "    frontier = {(path[-1], velocity(path)): path}\n",
    "    solutions = []\n",
    "    while not solutions:\n",
    "        frontier  = expand(frontier, legal_moves, track)\n",
    "        solutions = [path for path in frontier.values() if is_solution(path)]\n",
    "    return solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solutions!\n",
    "\n",
    "We are ready to solve the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solutions = search(track)\n",
    "\n",
    "plot(solutions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the fastest solution is 12 moves, and there are at least 7 ways to get there (with perhaps others discarded).\n",
    "\n",
    "# Submitting your Answer\n",
    "\n",
    "I'll need a bit of \"tricky work\" to put my answers into the form requested by The Riddler:\n",
    "\n",
    "> Finally, submitting your answer can be tricky work. Please be sure to submit both your total time, as well as your sequence of moves. Each move should be assigned a digit from 1 through 9, corresponding to the nine possible destinations of the move:\n",
    ">\n",
    ">     1 2 3\n",
    ">     4 5 6\n",
    ">     7 8 9\n",
    "\n",
    "I already started the tricky work by defining the nine `accelerations` to be in this order. I finish the tricky work by defining two functions to translate back and forth between my `Path` and The Riddler's `Digits`: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Digits = List[int] # each int is 1-9\n",
    "\n",
    "def digits_from_path(path) -> Digits:\n",
    "    \"\"\"The digits that the path represents.\"\"\"\n",
    "    return [1 + accelerations.index(velocity(path[:i + 1]) - velocity(path[:i])) \n",
    "            for i in range(1, len(path))]\n",
    "\n",
    "def path_from_digits(digits, start=track.start) -> Path:\n",
    "    \"\"\"The path that the digits represent.\"\"\"\n",
    "    v = zero # Starting velocity\n",
    "    path = [start]\n",
    "    for d in digits:\n",
    "        v += accelerations[d - 1]\n",
    "        path.append(v + path[-1])\n",
    "    return path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 6, 3],\n",
       " [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 6],\n",
       " [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 3],\n",
       " [3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 3, 3],\n",
       " [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 9],\n",
       " [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 6],\n",
       " [3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 3]]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[digits_from_path(path) for path in solutions]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Alternative Solutions\n",
    "\n",
    "I have identified six different opening sequences of moves that each lead to solutions with the fastest possible time of 12 moves. I don't understand exactly why in each case there exactly 7 solution paths are reported; I suppose it is just because the finish line is crowded and there are only so many ways to get there."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tkiE4fPgwTU1N0XbDkIhYB0GgqCoP/0Ojra1N7l0HiYh1AKxdvor996zj5APbyUrM5VTbCTrNJurq6qLtmqE4evSo79517fJVmDAzfthU9t+zjrXLV0XZu9hFxBoiXXPWpCSk+TplF6QW886Dv5RHNQPEbrdTW1vrO6ZKKZRSpCSkUZJ0mQg2CDLqJkQCzVmTYLIwyTZtUHUPdT788MOgx1TmugmMjLoJkWDzrwxkXhbhHI2NjWE5prF8zoTDzh9Jg0Mk2PwrMi/L4HC5XHJMB4iINUQOOCpxubu3+LrcTva2VkTJI+Oz1/5+wGN6wFEZJY9iGxFriCxevZLK9h243E601rS6mqhoeRfXNROj7ZphMV0/lV327Witfcd0KE+k3B8i1gGwePVKTrXX0Og8Q8eS0bg+JkI9HxwOByXf/BxuOjnYvJuJTywSofaBiHWQSIf98CBvQwwdEesgGaqvawk3ctELHRHrIJHuheFhqL1M7nwQsQ4SEWt4kOMYOiJWIarI2yNCR8QqRBV5V1XoiFgFwSCIWAXBIIhYBcEgyBA5ISaQian6R4bICTGBTEzVP5IGC4JBELEKgkEQsQqCQRCxClFFGvlCR8QqRBWTSU7BUJEjNUgSEhKi7UJcYLFY+i8kACLWQSMnWXhISkqKtguGQcQ6SGw2W7RdiAsyMzOj7YJhELEOkqysrGi7EBdkZGRE2wXDIGIdJNnZ2dKSeZ5YLBbS09Oj7YZhELEOgPUPriYvaSTplmzaVleiyqqi7ZKhSU5Olsg6AESsIbL+wdVMaZtKgsnim0RppnsW7DwcbdcMS35+vjTUDQAZdRMixa3FASdRusQ9dVB1D3VMJhO5ubm+3zLqpn9k1E2IyMRU4SUtLY2cnBzfbxl10z+SBoeITKIUXgoLCyUFHiAi1hCpSqnqNYlSp9vFAdtB6c00QJKSkhg+fHi03TAcItYQWfjwcvbadtPqakJrjVt30tbZyvXf/Zo82B8gI0eOlEc2g0DEOgAWPrycAwde5NDW+1nHFlIt6ex+YSvjx4/HbDZH2z1DkJiYyJgxY6LthiERsQ6CThLZWryWFmcjlr2N5ObmkpeXF223DEFBQYH0/hokItZBcs2IEt5OKCfTksPuF7Yybtw4aTDpB5vNxtixY6PthmERsQ6S6y69k1+Pf90XXXNycrjoooui7VbMopSiuLiYtLS0aLtiWESsg2T06DmMM2t2mCvItOSw6/m/M2nSJDkZg5Cbm0txcXG03TA0Itbz4Lqc6fx0wh9pcXmiq81mY/LkydLY1IPExESmTJmC1WqNtiuGRsR6Hlx36Z04LC4OJh4g05LDv57bwkUXXURBQUG0XYsZlFKMHz++W9dCYXCIWAfA355cw+iqSkae+Yh/zJzLgdcPMsVt5pXCl3zRVWvNxRdfLCenl4KCAsaNGxd0/drlqzBhZvywqey/Zx1rl6+6gN4ZCxFriPztyTVkPf0EiZ1OFJDTepasp59g0f7hvJ/YTl12sy+62mw2Lr30UlJTU6PtdlTJzc1l6tSpQVvJ1y5fRUnSZSilfCOZSpIuE8EGQUbdhIj1uadJ6uze3TCp08m4jWcBODRxky+6dnZ2kpGRwbRp00hMTByUb0YnNTWVadOmkZycHLTMBGtJwJFME6wlIdcTy+dMOOz8kVE3IZLVejbg8vTWZqa4zWxsLKNxBL7oCp5udZdccsmQa1ix2WzMmDGj326Y4RjJFMvnTDjs/JE0OETqUwKfePUpmVyXM51Kk4v8mzO7RVeAoqKiISVYm81GaWlpSB31ZSTTwBCxhohj6VdpN3dP2RymBBxLv8p1l94JwNsf/LZXdAUYM2bMkEiJU1JSmDVrFvn5+SGVP2U/0WuZy+3kgKMy3K7FBSLWEPn4XUuo/+o9nE7JxA10onDlj+Djdy1h9Og5THGb2VBXzqX/uaBXdAVPhC0tLY3bRqfs7Gwuv/zykIe+nak5QV7ySJocZ30jmVpdTVS272Dx6pUR9taYiFgHwMfvWsKV5e+SsHkHv566mOSaY9h37gTwpcKnz+4KGF3Bcw87Z86cuHqso5Ri9OjRzJ49e0Ad9Ld//3ekJAzjsHUfE59YxOjHrmLiE4tEqH0gYh0EE4ansv+yBTSnpFP3s58D+FLhjRW/DBpdwfOe3NmzZzNmzBjD93SyWq1MmjSJmTNnkpKSErLdmZoTFCddzJn2k1z38H9H0MP4QsQ6CJRSXDu9kJfGzse+bRv2nTu7pcKJyUlBoyucay0tLS01bF/i7OxsZs+e3edz1GB0RdVjSVVY4/w+PpyIWAfJopIRrCuagyM981x09abCx2t29hldwfN2v4KCAubNm8eYMWMMM7wuMTGRSZMmMXfu3JAbkvyRqDp4RKyDZMLwVApGZLJp+vW+6HouFX6m3+jaRWpqKjNnzuTyyy9nxIgRMZsaWywWioqKmDdvHiUlJYOeUEqi6uARsQ4SpRQLS0bwTNo0VHYOdT/7OaNHz2Gy28yGU+UA/UZX/23l5+czZ84cZs+eTW5ubsy8hM1qtTJq1Cjmzp1LaWkp2dnZg96WRNXzQ8R6HiwqGUG7yUL1dbf4ouv1fqlwqNG1C7PZzKhRo7jyyiuZM2cOY8aMicpsdUopUlJSmDhxIvPmzWPOnDnk5eWdd5c5iarnhxpIN6jS0lJdVlYWQXeMhdaaa3/8d/IT4YGX7yexeBym/7mThZvu5Js5s1m66Nd02Ns59sAWLGYrJszYO1toGg2zvr4wpDqampqoq6vjxIkTNDQ00N7eHpauaz0xmUwkJSWRk5NDfn4+ubm5ffbrHShnak5w+kcVtLvsTH5ssYg1CEqpcq11aaB1sZFrGZSuVPipTQdJ/PxS7D9+gsLar/lS4aXArl9tIs9sw6w8hzolYRiJx53s/On6kASblpZGWloaxcXFNDc309DQwJkzZzhz5gxtbW04nU5cLteAfbdYLFgsFlJSUsjOziYrK4vMzMywCtSf7d//HZekXs7BhEqmiVAHRUTEqpQa1NXfiHaLSkaw+m8H+cekK7gs9znqfvZzrv/UdH5SX8bxmp2kHQNzj/vPBJOFtGPtA65v2LBhDBs2jNGjR6O1xm6309raSltbGx0dHXR0dGC32+no6GD16tW8+uqrbN682Rc1uz6JiYnYbDZSU1ODptnhPKbd7lUfC3yvasT//kLY+RMRsRplREM47CYMT2VcXip/3l/Pwjvu4OQPVvHxz9zLTyhjY8UzfNy8JOA2ks2hdzsM5GfXfWWwzggPPPAA8+fPZ/78+SHX01+dg7ULJaoa8b+/EHb+SAPTedKVCu84Uo9z4c2Yc3NQf9jiS4XtnS1B7ep+uYuOw40X2OMLi7QAhw8RaxhYVDICt4YNhxrIueMO7Nu28ZmmYipNLk7lNfWaI8fldnKs4xDOU3bqfrkrrkUrLcDhQ8QaBrpS4XWVJ8i49VbMuTlMe8+T9lRd/FfqRrXT6mr2jixppqxhL++deI2tjj+Rev1onHXxKVqJquFFWoPDgH+r8Gkn5HjvXW+YYmGDu5ylX/+1r6zWmqqnK7GWJ/DRwfW8qX7Bv93zAI5/NdC85Rh1v9xF4th00hYUkjjW2JM3SQtweJHIGia6UuG3dtf6oustO2y+DhJdKKWYf9tEktKnkF14CzUH9vHaE4+QWJrFiG/NIv3GsXERaSWqhh8Ra5jwT4VNSUnk3HEHGYeamHxUs7HimW5lU9ITuepzE2hpKGDK/KXUHNjHH3/wEM5OB8OuGBUXopV71fAjYg0T/q3Cdc0dvuj6xa1uX19hf8aXDmfMtBw+3J3F/C8s9wnW0d6GspgNLVqJqpFBxBpGulLhN/fU+qLr2GqN6yNnt1QYzqXDCYkmjlRm8In/uqebYAHDilaiamQQsYaRCcNTKc5NYd2uGgAybr0VlZXOp7e6e6XCcC4dPnmkibbWQhYtX9FLsGAs0UpUjRwi1jCilGLRJSN9qbApKYm8Zf9JSbXmg/KdAW260uEdbxwht2hGUMGCMUQrUTVyiFjDjH8qDJ7o2mGFf/+9gz2TJvPOZZPZ/NgXfeX90+FNa/YxfvYVfQoW+hdta8Upfjz9G7ww+xFOrNpBa8WpiO/32uWr2H/POkpSZtPpduFucUe8zqGGiDXM9EyF//7TZZhdYO30HOysJsh4YUc3wfqnw+//9SgT51zZr2AhuGjPvrKf3MRMlFJ0NnTQ8MeDERVs15w1KQlpKKUwmxK4JHm2zFkTZmSumzDb9UyFLa/uIKFHkEl0geXVHd2W+afD9Sdauwn27oXXBBUsdBetsiVAjz7j2umm6a0Pw7aPPZE5ayJn54/MdRMBO/9UOKMpcJnMHst7psNut/YJtnh4bp8R1rcNixndFnhsa2dDR5+2PRnIsZE5ayJn54+kwRHAPxVu6ONNozX3fRtHdbXvd890GAg5Je7CnBG4USfY8vPlg/e24daB3y8lc9aEFxFrBPBPhVs/WUpHjx7YHQlwaFwiTevXU7VwUTfR9kyHYWCCTbu+CGXp/rcqi4m064vCuo/gEarjleMoZaLT3T2iy5w14UfEGiG6UuGT1zxKwxcuoz4N3EB9Gmz/mIPvfKaTFx6ZS/rt/95NtM6jR3ulwxC6YFOm55Fxy3jqOs7i1hpzRiIZt4wnZXpeWPevS6jp1mx2ubaxq327zFkTYeSFaRFCa82CH20hd1giL98559wKtxuev5E1zQd4PN3GtYXX8r3J99D0m+c5+/Lv0S4X6TfdRMOVt/H2G6eYc0sxM64r9Jnvf+8frFv9OCMnTOaW+x7CmhT4tSxXX301AJs3bw77vvkLtdK1nRt/eG/Y6xiq9PXCNImsEaJnq7APkwlufoolza2sMOWxsXoj39n3BFn33kPxxg1kff52mtavhxWfY4TlFDv+dNiXDsPA72HDjQg1eohYI0jPDhI+ssbCgodYUlXGihHXsLF6I/f+/V7IyWT4ffdRvHED2Z+/neL3foZqb+HNRzfQfuRDn3m0BCtCjS4i1gjSs4NEN2Z9BQrnsaT8NVaULPMJ1ul2YsnLY/h99zFl/avMGHGCs53pbF72o24NURdasCLU6CNijSBBU2HwpcO4nSzZt4UVpSu6CRbAkpdH6f98haLJwzgy9iZOvF3WrfX4QglWhBobiFgjTNBUGHzpMAc3sMRhDihYpRRXL70ES4qVwzc+TObtt3drPR4zsoBFy1dwbN9u7l54DYmWBJRSbNmyhS1btqCU6vYZ6MxvItTYQcQaYfpMhcGXDvPmfSwZvSCgYLs6S5z6qI2a0tu6NURVLVzEsDf+wls7d1GYnckdV87CmhB8JrqTJ0+G7LsINbaQRzcXgGVrynhr70kUMDLDxorrJ/LJ6aPOFag/DL+YB0VXwG2vsGbvCzxe9jjXFl7LY1c9hsVkQWvNX56u5Oieej77nVlkjUjBeeoU9c8+y9mXf4+zvZ11VhPmSUUUpV7MJVnzSU5Iw+5qYvfprXx6zWO+6vr6z9cuX8UEawnJ5mG4dSdKmdjl2iZCvUDIo5so8nrFcTYfqAM8/euPN7Rx3x8reb3i+LlCfukw77/IkouX9IqwgfoOdzVEFW/cwP87e5brOzqZlFTCrNxPkGJJ97y135LOzOHX8b9L+hdboNEzWrvRzvBPhCUMnIhEVqPMI3Ih7Oat2sTxht4NP6MybLyz8ppzC7ydJajdDf9nG6SNZM2eNTxe9jiNOxupWl2FxWThwM5aNj67t1dnCaUUOWYzW7/+OimW3q8wdbo7ONpS1VU4oK8FKcVYTNZey1tdTUx8YlFI+xvL/4UR7C54ZDXKiIYLYVcTQKgBl3e1Dnc6YO3XQWtfhE2fle6LsIH6DndxurOT5ITAIwcSlJWLUsZ4PslFAT8JyhLQVkbPRM/OH3nJd4QZmWELGFlHZiT1LtyVDr95L7z/Iky/nSUXeya2erzscfg7PHbVY8y/bSIvPbKdTWv2ccuKmZhM5yKl3dUUMLLaXU1M+tFiIPiJs/+edaQEELuMnokN5J41wqy4fiI2S+/W2eLc1MCiuexOX+swTZ4W5J73sNZhpl5D6brYfXprwLl1dp/e2q+vBxyVAW1l9ExsIGKNMJ+cPoof3FLCqAwbClsY2+sAAARQSURBVBiVkcT8CTn8/eBpHvnz3t6CDZAOQ2/BFs3ICpgOf3rNY5Sf3ECrs9EzAsbZSPnJDd1ag4OxePVKKtt3yOiZWEVrHfJn5syZWjh/3G63fmTtHl1475/1Q2/s1m63u3eh936h9YNpWv/zd90WP7/7eT31uan67rfv1g31LfpX39ii/7Bqp1bKpPE0OPf7EWIXoEwH0Z/cs0YBpRT3L5oMwLNbjwDwwI1Tur+n57I7Yd8bnnS4+GOQNhKg+z0s8JXPfpNNv93PzXO/xOvvPNtv3cOHDw/nrggXEEmDo0SXYL98xRh++86HvVPiIOkwdE+Jf2X/IUXTsrn+0s9zpqbFdxXumvW859W5tjZAt0fBEIhYo0i/gu3RWcIfn2CPbmRz0cu93iwhxB+SBkeZflPiIOkwdE+JbZdk0/HeDN7/69FunSWE+EEiawzQZ4T1T4ffWN4tHYZzEfY1/Twto2rZ8cbhXp0lhPhAImuM0GeEDdBZwp+uCPuU8yk+X/cAf3t+L6Do9bZvwdDIqJsYQ2vNo+v28ezWI3xpXtE5wQboO9yTNXvW8Nqbf2PBwS/SYbJjddtoS2qiYIGNW2+8IQp7IwwUGXVjIIKmxP2kw+CJsNNzpuPGTaI7GYUiuT2d2vXw+z+/GYW9EcKJzHUTg3Y9BZt97TKPYLvS4UMbe7UOd2GrKMTU429NcFs5+teBvfIlVo/NULPzR0bdxKidv2DTSm8+F2ED9B32x9YeeNRNsOXh8FXsImfnj6TBMUzAlFipPtPhtqTAM2EFWy4YBxFrjBNQsJljgqbDBQtsuEyObstcJgcFCwK/uV8wDiJWAxBQsJd9BQrm9kqHb73xBvIXQrOlHo3GntRI/kKkNTgOkOesBiHgc9ibn0L9Yp4nHb79D77Xtdx64w1c/cTVQGTmuhGig0RWA9Erwr7bjl7wYJ+tw0L8IJHVYPSKsHOv4IGCOagAfYeF+EIiqwHpFmHfPcqTw+5G99FZQogPRKwGxV+wPyp38eaIZZIOxzmSBhsY/5T4a1vdbM6ZRsGbK1HFH4uyZ0IkkMhqcLoE+x9XFLPkzBdxOTrQbyxHRtzEHyLWOKBLsAvmzeF7jltRhzby2lUH2TS/gtqHxrHzjWei7aIQBkSscUKXYPOH59OpFZmmVkwK8qljavn9Itg4QEbdxJGdUopP1v8Ws+qeAtuUg9H/fDwidYpdZO38kVE3cWaXp+uCLD8dsTrFLnJ2/kgaHGecUrlBludcYE+EcCNijTOOzVhBm+4+bWObtnJsxoooeSSECxFrnDHrpmXsnvkoteTi1opactk981Fm3bQs2q4J54m8ME0QYgh5YZogxAEiVkEwCCJWQTAIIlZBMAgiVkEwCANqDVZK1QHVkXNHEIY8hVrrgD1bBiRWQRCih6TBgmAQRKyCYBBErIJgEESsgmAQRKyCYBBErIJgEESsgmAQRKyCYBBErIJgEP4/OB9UFP1vzJAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "openings = [3, 3], [3, 5], [3, 6], [6, 2], [6, 3], [3, 5, 2, 4, 4]\n",
    "\n",
    "for digits in openings:\n",
    "    plot(search(track, path=path_from_digits(digits)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizations and Tests\n",
    "\n",
    "To gain more confidence in the code, here are some additional visualizations and unit tests:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test_intersects(expected: bool, segments: List[Path]):\n",
    "    \"\"\"Test if [p, q] segments get the expected result from `intersects_circle`.\"\"\"\n",
    "    plot(segments)\n",
    "    for p, q in segments:\n",
    "        assert intersects_circle(p, q) is expected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_intersects(True, [ # Line segments that intersect the circle\n",
    "    [Point(-2, 3), Point(5, 2)], \n",
    "    [Point(-1, 5), Point(4, 0)], \n",
    "    [Point(2, 4),  Point(2, -4)],\n",
    "    [Point(-3, -1),Point(1, -3)],\n",
    "    [Point(-6, 0), Point(7, 7)]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_intersects(False, [ # Line segments that do not intersect the circle\n",
    "    [Point(-2, 3), Point(5, 3)], \n",
    "    [Point(-1, 5), Point(4, 1)], \n",
    "    [Point(3, 4),  Point(3, -4)],\n",
    "    [Point(-3, -2),Point(1, -4)],\n",
    "    [Point(-7, 0), Point(7, 7)]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Waypoints on a line segment\n",
    "p, q = Point(-7, 7), Point(7, 0)\n",
    "plot([waypoints(p, q)])\n",
    "assert not intersects_circle(p, q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's a visualization for `expand(frontier)` showing the first six expansions.\n",
    "Note that the growth in number of paths is much slower then O(9<sup><i>n</i></sup>). After 6 moves there are only 1,107 paths, which is 500 times fewer than 9<sup>6</sup> = 531,441."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "frontier = {(track.start, zero): [track.start]}\n",
    "\n",
    "for i in range(6):\n",
    "    frontier = expand(frontier)\n",
    "    plot(frontier.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Different Track\n",
    "\n",
    "Although the code here is not ready to handle large, arbitrary-shaped tracks, it can handle some minor track variations. Here I define `track2` to be a track with a larger central circle, and a circular ring of valid points rather than a full rectangular grid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XsqonWZffDRixxgrbRxMqwNJ774g6edySV8DC51+Jq+5YZW63m9raWo4fP87p06c1b0U7Q2pqKoMHD2bo0KEUFBRE7GYnhODNJ34d08omcqjL43bz/F234WxtjTjXkl/AwudeiTjelwyYaHBnhAqxl181N0Qej3e5mNfrpbq6mgMHDlBfX4/HE5lpsL9js9k4dOgQx48fp6ioiJEjR1JQUBAo939ewVb2r0s2kVv+Fjc/9IOELt3TGww4bbao52pt+V2/3uumPaECWPLyo14X63h7SCmpqalhw4YNbNy4kZqamgEp1GBcLhcnTpxg/fr1bN68OWSYCGBQ6QjufOURBo30eWvVh6by+zt+TvWxQwltRyK/576k34q1I6ECjJl5acQxg8lMxbz5nbpXQ0MDmzZtYv369Zw8eRK3OzxDxMDG6XRy+PBh1q5dy44dO2hqagopv/nBH3D9kqmkOtYGrOxbTzyesPtXzJuPwWQOOaY3GDr9Pfc1/VKs8QjV0drK3nUfk56dgyWvAITAkl/QqaBDa2sr27dvZ+3atRw9ejRpxkaTFbvdzr59+1izZg179+7F6XQGynrSyo6tuIyrFt6HJb8AEOj0BnRGI2UTp3S77t6kXwWYID6hAqxa+gyff/Av5v38cQaPHtOpe0gpqaqqYvfu3Zw5cyYRzR5wCCEoKChg3Lhx5OeHuqM9HTGuOXqY1x/+LqNnXMKXHngoYfUmgn4fDQ4eiPdNIdSTlftRTKEe3b6Ftx57hKnXf4XZX7uzU/dqbW1l//79ypImCLPZzKhRoxgxYgQmkymkLHxcVpfZirNpSkKW363/0xt88uYb3PDgj5NqplN7YtW8G+yf4uYy54EQSJ0RIT14XdGDO47WVla99Ay5g4cya+7X4r6PlJKTJ0+ybt06Dhw4oISaIBwOB7t27eKTTz6hri40Ohvel22xfyHwPbvMebScrWD5gw936b7Tb5pLQdlw3n/5OWzNTR1fkARoSqzh43UA9vpJoetRAakzYq+PzGIghOCj136HtaGeqxd/B0PQL3m0ugP3sNvR6XR89tlnyu3tAfyR9PXr17N3796Q78LflzU4myJW9Hj15ojvub3vMbhcbzBwzeLvYLc288ErL8V1bV+jKbFGc9ldpugJyKIdP7JtMzv//U+mXHdjRD81VnegqamJzz77jJUrVypr2sP4reynn36KLWxs1G2MPiMq/HvuzBhtYdlwpt/0Vfau+4gDn32S9HOzNSXWaAQvZ2vveFfc35qaGj755BOqq6u73U5FfHi9Xo4ePcrGjRtDvJh4v+fOoiV3WPNiTcnbCjJ0rq3O4/AdDyKW+xsNKSVHjhxh48aNEWOCit6htraWTz75hKqqKsD3Pes8oVM2hdcd8T13lmjucLKiebHO/PpXQILObQMpMTrqI3L+HN2+Jab7G47L5WLXrl1s27YNu93e081XtIPVamXTpk0cPHiQrz3+S9Kz1mB01IOUCK8LvB4uuO7ybt8n3B1OVjQ/N3jdsrdBdyUlk49w3d33tR09l++nM+6v3W5nx44dHD9+POn7LwMFh8PBjh07aG1t5fZf/wK93peM7eO3/5dd7+Ww+fe7GT9rdreXMU6/aS4HN23g/ZefY+iYcUm5BlbzltVdX4zJUcc131wUtTxe99dut7Nt2zaOHTumhJpkeDweDhw4wM6dOwNTOS/9yn+QYvwYe9p43vjRkm7fQwvusKbEGh5aP7h9E46UMeh1uzAYjRHl4e5vrNC8zWZjy5YtVFZW9ljbFd3D6/Vy8OBBduzYEYjK3/6bR0ixHaT17MVs+/B9IP6hm2gUnTciqd1hTYk13OKtW/Y2UqencFpBRHk09zeaxbTb7WzdujWQslORvEgpOXz4cMDCmlJSGPVlC1IY2Pz73bjbUrF2VEd7ZckcHdaUWMNpzwWOx/31u75KqNrBL9jPP/8ct9s9oNxhzYo13AUOJp7or8vlYvv27cr11SBSSg4dOsTu3bvxer1R3eHukKzRYc2KNdwF9hNP9FdKyZ49e5RQNYy/D3v48OGo7nB3SUZ3WLNiddcPjuoCx+P+Hj58mIMHD6qor8bxeDzs3r2bU6dODQh3WJPjrD4X+HxSPGsxGOeeSyfalvzsvElTY7q/1dXV7Nq1a8CnXOkvOBwOtm3bRmpqKrf/5hFeXbScVrfPHZ4458pu1e13hz958w2O7dyKrbm5T9OYatKyBrvA/nSiwVkKK3ftZM+a1RHXnT17lu3btw+oTIMDAavVyrZt2/BImXB3OKuwCITA1tQEUtJcV8uqpc9Gfb56mqQTa3vjYP6yYBd4zYrlEXl/3U4Ha1YsDzlmt9vJzs5Wc337KbW1tXz++efMvvm2dt3heJ6vYNatfM23DWgQ0Z6v3iDpxNrROJjfBfZHgWOmEw06LqVk165drFy5MuHtVSQPx48fZ8+ePe1GhzuTxhTaSVfbB2lMk06sHREeBY4nzWRlZSXHjh3rlfYp+g6v18v+/ftpsloT5g4nUxpTzYk1PApcMW8+On1onCw4najVamXPnj0qoDRA8C9gn3HdzQmJDkdNY2o09kkaU02JNdwFBl+aycKy4QidLiKdqJSSvXv3qn7qAKO2tpZDhw4lZLJEeBpTEBSUDu+TaLCmhm58LvCVFE4O3YrhbO1pxs6azbX3fT/k/MrKSo4fP97bzVT0MVJKDhw4QEFBAaO+bGHXe4ZuLaUbW3FZQJxrVyxn47t/oq7yGPklpYluertowrIuf/Bhlt7xJ6ytV4DXQ93+c3N5G05WYms6y9BxE0KuUe7vwCaaO/zbu9/juUX/Zukdf+pyVsQpX7oRozmFDW+tSHCLOybpxRqeahSdHlvzpYEPu3LXTgBKyi8IXCOlZN++fcr9HeDU1tZy5MgRRIoE6cVjzOh2GtNUSyaTr72efRvWUlfZu0HLXhdrZ9cbRks1GpyCsnL3Tix5BWQVFgWura2tVfN+Fb6hvoMHcTZOBhH6qHcnjWks69rTqUx7XaydXW/YXqpRKSWVu3dSUj4+sC+nf4K3ShuqAN8OCvGmq4332Uy1ZDLpmusirGtPzzVPeje4vRSU0fqr1dXVnD59ureap9AAPZHGtC/6rkkv1mgpKP2pRsP7q263mwMHDqgtFxUheFPXx3yGukpaZlZU69qTJL1Y5z/5GOlZa9C7rAAYnGcCqUaD+6sAVVVVEfulKBR5l81EZ1oVSGOK9JKa8XGXN7Xy09vWNenFCj7BpuVsBKD8Ojfzn3wsor/qdDo5cOAAXq+3g9oUA5HcOTOZsHAoOUVrQOhIzUnrdp0B6/rJGl5c9HX+e971LL33jh5bkaMJsUYjvL966tQpGhsb+7hVimTm9OnTTPnqLejdNqyHEjMfyJLnm6DTcqaxx5fQJf3QTSyC+6ter1fl+1V0iMvlotXpwuTahcs4nuawHQG78mx++uc/RRzrqSV0ST90E4vg/mpdXR0NDd3boEgxMDh58iSmEiseQzp//59nQsq68mz25hI6TbrBgf7quAkIITh58qQaV1XEhc1mY9z11yTMFe7NJXSaFKu/v1pSPgGr1RrYaUyhiIcGqy2mK9xZfEvoQhPzBS/RTCSaFGugvzpuAqdPn6a1tbWPW6TQEmfPnsUwpCmqK9xZxlZcxqW33xl4HbxEM9FoU6y7d2LJLyAtJ4+jR4/2dXMUGsPj8TBk9iUJc4VHTZ8JwJXfupeFz73SY2tdNSfWc+OrE2hsbFQraxRdwuZyY0yQK9xbaE6s9qazgf5qQ0ODmlqo6BJ2ux3j4LMJcYV7C82NszbVVAMwZOw4Tp06lbB2KQYWUkqGXTEnxBXu7rN59913J6x90dDcOGtz7Wks+QVIUwrNzc2JbJpigBE+QaK7z+aLL76YyOZFoCk3WEpJU81pSsoncObMGZVZX9Et7HZ7wqLCvYG2xOptwO2wU1I+QbnAim7j8XgYec2VCZ0r3JNoSqxely9VS27ZCDVpX5EQrHZnwiZI9DTJ/3MC7Fmzmvqq3Xg9LhCCIzu34XCpSfuK7mOz2fDqWvAY0ln+w80YnQ2k5G3t9lrXniDpLat/lzivp23ur5R8tvJVmo4e7NuGKfoFp1Z9iMtwse9FNzMf9jRJP3QTbZc4j8vF2c+3JLxtioGHrnUmXn3o3N5omQ9BDd10WB5rqZGntSVhbVIMXOLNfAhq6KZDYi010qel93JLFP2Rnsh82FMkvVij7eIl9Hqyxk/uoxYp+hM9kfmwp0h6sfp38RI6PQB6s5mcKTPJGDa8j1um6A/kXTYTYVqFweWbDWdwng1kz0w2kl6s4BNsRvYQAAounKqEqkgoeXNmYi7wZc8cOr0qKYUKGhHr8gcfxtkyAoCmncXUr17fxy1S9DdkN1LYHtjoex7f/+1zAzsVqX8XOf/mVG6jBem6SglWkVC8smti3bNmNR+//vvA6wGdijTWLnI628yEt00xcInHsEZ7dn3zAJwhxwZsKtLOjIMpFF1FxmFZVSrSDtDSOJhCy3RtrrlKRRpErF3kvKmqz6pIIF1cFzLzltsijg3YVKT+XeT8gjW4mhHGVeRdpvqsisTR1TVc5nTfTLrUzCwQokdTkWpiidz8Jx9j6eJ7cDhAV7aP3HFKqIpE0zW57t+wjhRLJne/uBydXp/gNoWS9JZVoUhWXE4HhzZ/yqiLLu5xoYISq0LRZY5u24zLbmP0jEt65X49Itb2xlITteWjQtHbhD+bfhd42LgLopa3d21X6BGxtjeWmqgtHxWK3ib42YzmAnfnuY8H5QYrFF2gt11gUGJVKLpEuAvcGyixKhQAxN+n7O0osB8NilUFoBSJpzNPVV+4wKBBsaposaJH6MRj1RcuMGhgiVxkueZ+XxSaoGO1CiHadYF72pAk/RK5cHQ6ZVkViSceoUkp23WBe3rYUXNmSnnBip4gXiPQVy4waFCsOp0m1h4oNIYuju5VX0WB/WhOrAaDEqsi8Yg4LGtfRYH9aE6sZpOxr5ug6IfodB1LoS9dYNCgWI0moxq+USSU+g/XYzt9EQAnNg6O2EFuz5rVLL1nAXvXfYTH5WTf+o/7opnaE6vBYMRoVNZVkRjqV69HOq/CbbQA4DZlhWz56N9y1J8AzWW391iq0Y7Q3Dir0WjEZDK1e45CES8628yoqW79Wz5G23I0VqpRNc4ahk7oyMzMTGSTFAOYjlLddibVqBpnjUJursoZrEgMHaW67c1Uox2hSbFaLBYVZFIkBG/aenSe0Iz6wVs+TrzquohreirVaEdoVqxms7njExWKDii7/mqM3rW+F1JidNSHbPlYe+wwOr2BjNz8Hk812hGamGGwdPFimhtqANj53iqObNjM+fPmYbfb+7hlCq1TVFRElU6A9PKl7w6ibMwVwK0A1J+oZO/6j5l2w81cetuCPm0naMCy+oR6CvBF5KRspbnhFLtef71vG6bQPDqdjsLCQqRjKGZ7JWVjxoeUb3h7BUaTmanX3dRHLQwl6YdurI0NgDvsLDf2prNqvFXRLVJSUvDYrThSytDpj4U8e36rOvGa60jLzAL6PjNn0g/dSNkS47wW0tLSEtYuxcAjLy+PT998G6kzkjZMhDx70axqX2fmTHo3WIj0mMeLi4t7uTWK/kRRURFNB1tBepkx7+bA8WhWNRlIerFm5OQSGQczkJGTS35+Pvo+WKqk0D5ms5mcnJyo/dVk66v6SXqxLnzhBSy5xSEWNsU8iIUvvEBubi4ZGRl92DqFVsnNzcXZ0hzor/pJVqsKGhAr+AT7vRV/ZNrNXwXAIHzTDc1mM8OGDevLpik0iE6no7S0lI9fey3QX/WTrFYVNCJWP5OuuBYAlzcdt8s362TQoEGkpKT0ZbMUGiMjI4PCwsKI/moyW1XQmFgtefnoDSZcsoG/vfgcANnZ2RQVFfVxyxRaYtiwYZjN5oj+ajJbVdDAOGt4WckFF+J1naB2y9nA8ZKSEhVoUsRFSkoKxcXF1FZVhvRX609Usnvth+1aVTXO2olyKSXlMy8FHLi8xQFXuKCggKys5HNbFMlHYWEh2dnZfPRqaH91w9srMKektmtV1ThrJxlaPgEAp2gKuMIGg4GysrI+bJVCC+j1+kBAMri/Wn8yufuqflXIO/QAABe6SURBVDQnVktePum5eXhdx6nb2hQ4XlxcrBalK9olLy+PgoICgJD+6oa3kruv6kdzYgUYPnEK0l2JW44NuMJpaWmMHDlSrXNVRMVgMDBq1CgMBkNIf1UrVhU0KtaS8glI3Dj13oArDDB06FCys7P7sGWKZKWoqIhBgwYBhPRXtWJVQaNi9fdbpesodVvPRYXNZjOjRo2KKwesYuBgNBoZOXJk4Lnw91fLr6jQjFUFjYrVkpdP9qBipHMfHsYHXGGAwYMHk5eX14etUyQbQ4cOpbCwMPDa31+t3LpZM1YVNDjO6qekfAIe2YDTmB1whYUQGI1GRo0apcZdFYDP2xo+fHjgdWFOFo6UMqTYm/D1qmqcNUZZSfkEpPSAuzrgCvvLi4uLA/0TxcCmrKwsJBvm8z/6EVJnxGU8lfD1qmqcNQb+fquwbYlwhXU6HWPHjiU1NbWvmqdIArKzsxk5cmTIsaaDrXjdddiaGzXTV/WjWbH6+61eYzUuU25IVBggJyeHMWPGqGDTAMVoNDJu3LiIbCLSMRTZslpTfVU/mn6SfUM4TvA4QqLCfsrKypQ7PEApKyuLyCRSW1WJzZiJy1upOasKGklFGouS8gns/GAVJs9e7GmzeG7RvzE6G0jJ28r8Jx/DYDBQXl5OY2MjNputr5ur6CWys7MZPXp0SMBn6eLFWBsbkdIKwO6P1idFetHOoGnLGpgnrHeCTg9C4DLnhewCptzhgUU099efztYvVICWMzUsXby4L5rYZZLuCY536AZ8/VYhLHg8VSHHg3cBg3Mu0dy5cxPbWEXScdNNN0W4v7HS2fqOn6Ovh2Y6IunEGu/QjR+dsRSv+wRSekOOB+8OZjAYmDBhAqtWrUpcQxVJx6BBg7DZbBGiai+dbejrvh2a6YikE2tnMZID0oH0hG7BF747mMVi4cILL1QpYPopWVlZUb9fn8CiJ4OPleY2WdG8WNPyagHwuivPHZQS5IGIcwsLC5kwYQIGg6bjaoowUlJSmDhxYsQSSSkl6/74KuACwl1YQ1uaW+2gebHe8fST6A0mcB5u2wWsAZO9Cpf5IpY+/FTE+aWlpZx//vl93v9QJAZ/Fyd47i+cE+rGd1ZSOnEK+pSrEMKXtlaIdCy5xSx84YW+aHKX6RcmpvzSOezfuI7FL8xBZz3N2acv4c2DD2Kvn8DSh59i4WPfDZwrhGD06NFYrVaOHTvWTq2KZEcIwahRoygtLQ05HizUC664hpO7T2JMHUfZTB1fWnRvH7W2+2jesgLo9AYcLS089R9fZul//piq4d/k1mFLMNsP4GoTbDAGg4Hx48dH/BortMWwYcMivKRwoV75rXvwNAzB5Kjj6jsX9mFru4/mxbpnzWp2ffR+4HVzXS2r/rmFk5ZZ3HreY5jsB6MKNi0tjSlTpgTSfCi0RUlJCRdeeGHIToLRhHpo5xYcKeej1+3CoPFdBzUl1mj9zDUrluN2hm4z73Y6WHPUQpZZcOv0P2OyH8JVP4Hv3RT6y5qRkcHkyZPV+leNMXToUCZOnIjZbA4ciyZUodOxbtnbSJ2eoot8XlRnxvGTDU2JNdo4V3N9XZQzobmxEa75Fdk167n59hZM9kOMKJwbYWEzMzOZOnWqEqxGGDJkCBMnTgwZooklVAB3/eAQF7iz4/jJhKbEGg1LXn7s4xNvg1FXk/vp49z04ykBCxtLsMolTm5KSkqYPHlyyNLH9oR6cPumfuMCQz8Qa8W8+RhM5pBjQui4ZN58EAKufxr0JvLX/pQbH7+xQ8GqoFPyIYRg2LBhnbKoQIQLrHU0L9axFZdx1cL7sOQXgBCY0zN8Uw/9Lk3mYLjmV3B8PQVH3ubGJ74SU7AZGRlMmzaN0tJSNfE/SdDr9YwePZrJkyd3SqgQ6QJrHdEZP33q1Kly06ZNPdic7uP1evjjkv+k/sQxFjz5PBm5eT7hvvFVOPIxLF5HrSeTdx96G2fKCHSurejlebhMORidjTCkkjuX3M++ffvYv38/bnf4BHBFb2E2mxk3bhzDhw/vcHgmXKgHt29i1XONpHjWcufvftbbTe8yQojNUsqp0cr6nfnQ6fRcffe38Thd/OvlZ31BgyB3mD/fR0F+Hjc+8RWM9lN4jZNxmXPbltfl4jk9ht8veYby8nImTZqk5hL3EZmZmVx00UWMGDGi00KF/ucCg8bEGu8SptzBQ7jkP+ZzeMtn7Fmz2leYOZgFf6yG4+vh05coKCwAXapPyEF49WY4WYIQgrKyMmbMmEF2drZaXteLzJ07lxkzZkRk+YhHqP5nIJYLrIZueonOLGGadO31DD6/nA+WvYS1oR6AZVsdMOpqeP9nUH8Ilyknaj3BxwsKCpgxYwbr1q1T/dgexmAwMHz4cGw2W8SugPFaVCllu1FgNXSThMTjDhudjVGvNbitIa8tFgsXXXQRF154ocqY2ENkZmYyZcqUiEASxC9UP/3RBYZ+LFaI7Q77o8OpuZ+i8zhCL5Je3EYLy+76H6qPHgkcNhgMjBw5klmzZjF48GBlZROEwWDgvPPOY9asWQwbNizKwvHOCRX6XxTYT79/4qK5w/7JEl/PWY4pbxtGR0Nged1psYEWxye0irH8+efbeO/5V0Lqy8nJYfr06crKJgC/NZ0yZQoZGRkR5V0Ran+bCBFMvxu6iUZD1Ule/cH9DJtwITf+4BHfr3dTFTw3A4rGwYK/QdtDYHN6uGv5Juzb13NNcz6OlCGkez7nmh9fz6Cy80LqbWxsZM+ePVRXV+PxePrirWkSo9FISUkJ559/flSRQteECvCH7z6M1XYlZZP2aHI5XHtDNwNCrACb//YuHy7/Ldfe+z3KL73cd3Dr6/DneyAlG+xnIWsoXPEItjE3c9fyTXy2/wTftx7G7Z6I3m1l2NQzXHvPHSH1ejweqqurOXDgAPX19Xi93ih3V4DP5S0qKmLkyJEUFBREuLx71qxmzYrlNNfXYUpJxWlrjVuoyx98GHv9JF/uLeklPeMDFvzmVz35dnqEATXOGouo7rDeCEIH9jOAhLOV8NcHSN37Fi/Pn8q00UP5VVY55qn16L0tHN5RGtGX1ev1DBkyhFmzZjF16lRycnKSfgigt9HpdBQWFjJ9+nRmzJhBYWFhVKGuWvoszXW1ICVOWytCp2PImPK4hNpytgKXOc8XRNTpsTVfGkhH21/oV2JtTyQ6nZ4Hnno+NDr8759DWFZEXDb4989JNel5ef5UZo3I55dHLPxw6ytkp26L2pf1715XWlpKRUUFkyZNisgHNBARQpCbm8u0adNCAnOxlzqGBvuk18vaP74atd5g7PWTfOPjQYSno411rZboV2LtyKWvbbaGRofPnoh+YtvxYMFmfvF7mL82l6k3uCKsbPB9zWYzI0aMoKKigsmTJ5Obmzvgtp80Go0UFRUxbdo0KioqGDZsWEiSuqhLHetqo9YVbQlk+PXBaWc7Op7sY6nt0a/EGg8h7nBqafSTDGZoOgWECvahN7dzvPgCbn/mxphW1k9aWhojRoxg9uzZXHzxxZSWlvb7qYtpaWmMGjWKWbNmcckll1BaWorJZGr3GpfTwUev/T5meawlkMGEj4v7CU9Hq3UGnFhDJks0XYw0hA2/6IzgccPz02H7CpAyQrB/23+G25/6XlQrG47BYKC4uJiLLrqIiooKJkyYQFZWVr+xtgaDgdzcXCZPnszs2bOZOHEiBQUFcY1DV+3fy6s//Dab/vo2JeUXYAgTtsFkpmLe/HbreO0/f4rbkB7RndF5HKTkbe38G0piBkw0OJxAdPiGWZTXvO5zfduiwQyZAu/eA5UbYPQ1cN3TkFkcGNZZd6iOJ265kFumDMXWbOXtR5ZytmVCzIhxOA6Hg8bGRurq6qiursZqteJyuXrpnXcfs9mMxWKhuLiY3NxccnNzO5WL2eV0sH7l62z+v3fJyMvj6kXfpvSCiSHRYEtePhXz5jO24rKY9bz2nz/lbMOlpNiPoM86jLN5Ci5TbsjmZFpDDd1EIepSupATPLDxRV8QymCGax+HC76KzeWNECzAp//3d3a82YAjZXDMcdlouN1uzpw5Q0NDA6dOnaKpqQmHw5FUfSudTofZbCYnJ4fi4mJycnLIysrq0iyuqv17+ccLT9NYdYILrriGS792J+awPVTjIVioV/1kNiWjzu90HcmIEmsMGqpOsuz796DX63G7XdF/zesPRVhZW0phVMGGW9mUlMM47KW4jDkYXY0Unl/DjT+8J2Z7pJQ0NTXR3NxMc3MzDQ0NNDU14XQ6cblcvSJgnU6H0WjEbDaTnZ1NdnY2FouFzMzMmBMY4iGWNe0K/VWooMQakz1rVvOPF57GGzT7yGAyc9XC+0IFG8XK2sbcwl2vbo4QLPis7Na3WnGbQ6OROo+D4pFH2hVsOC6XC6vVSktLC83NzTQ1NdHa2orD4cDj8YT8xfNd6nQ69Ho9er0+8H9qaiqpqalkZWVhsVhIT08nPT09YduMJMqaQv8WKrQv1n6RkT9ehBAhD/SaFctDhAptaUxXLA8Vq06PmHkfsu6gz8q+s4jU0e/w8k3/zV3vwPdX+gIZfsFedN0X2fb2mxH39+rNVO8fgsPmxpx67qMPb1cwJpMJKSU5OaHL+TweD06nk7S0NGpqanC5XLhcLrxeL1JKfvGLX7Bs2TIOHjyIEAIhBHq9HqPRiNFoxGQykZWVhcfjienOtteu9sr85U6HPcSa3vLjX1J6wcS4ro1WHhCq7QhX/TS6UDuqW8sMKLGGf4kx05hGGfMLXHvH3wNWNvXlmfz+C//FnXI4D725HTgnWJcx+lpZj9HC7773MQXDLAwencOQ0dnYW2MHl2I9eH6LGKv8yJEjzJ49mxEjRnS67njKO7r25L49vPrDb0e1pl25b4hFjSHUeOrWMgNKrOFY8vJjDsZvee8vTLr6usipbjo9XHyvr//67j2Y/rqYP4y8mm+XLQgRrNHVGHVQ3uhsYmjdp1jTZrLjhJVt/zqOEISIt3hkdojl1RLhfVO/Ne0O/d31jRdtPhEJomLefFYtfTZkmpvBZCK7eAirly1l/4Z1XL342+QMGhx5cd6IgJXV//vnPGPYwLhBi3joTd8ve+H5NZw6mB4yDU7ncVBneJss3U4u+Ns7yKxc5M130Tx8BqeOtbJjdaWmxZvIvqkfJdRzDOgAExB1bG/MJXPY9dG/+fAPL+Nxu6m47RvRrayfoIjxlpTpLD47n4dumYPh/b9Qs68wJBo8+ltzePCjBzEfOMGDO0vJ3XQQXWYmuQu+Qea826mt9XJyfyNV+89QfeQsXrfsknjnzJkDwIcffpjYDywKiYz0BjMQhaqiwV2kuaGOfy19liNbNzFkzLjYVhYCEWP575/T6jHwU+fXuei8fOaceJFCWUuNKKBy8kNMu2ERzc5mlqxfwqpjq/iKZyLf+DQFx4drA6LN/frX0VssuJ0eqo80dVq8+zdW8+7S9aQZsrDkpXDxl0cwevqg6O3uJOE/buPnXMne9WsSYk2Dl7kZ3FbchnRS7IcHjFBBibVbSCk7bWU97yxGf2IjHinQi3Ofr02a+HzKL5l2wyKklKzct5Jff/ZrclNyeXLQYvL+9wOsH3wQIVo/8YgXJDs/PInHdW76ncGk47Lbx3RbsP5lbOGrY8wZFq7/9g+7ZU39y9xCVs9IL+nm91nwP//V5Xq1hhJrAshKS+GVR34U1cpGDBd4PTT9vIRMWiLqqaaAQUsOBl7vrt/Njb+7kbRBaTww+QHmMY36518MiPbpw4d49siRENH6cTs9lJ83lVdffCtEvNHIyDXzjcdmhRzr7BDK0nvviBqQs+Tls/D5ZXHXHa1s6R1/8q1HDcPoqGfhK7fGbGN/Q42zJoCzrfYQK7v8ofsDVjbiodTpyZAtEGXpZJGshU+eh7JLoGg85XnlbP7OZpasX8JTm59i05AKHv3No+QfrKLu+ed5oKmJg1dcGdXSGkx69p88N1nd7fTw0gMfRW2/tcERcawzQyhSytjL2PyL+eOsO7js80/WsumNv+EyXRn13FjL3wYiSqydQAjB+DlXUnrBRP619Nl2I8Y1ooBBRD7cHnQY/vmfvhcp2VA6C0vZJTw5ej4ri6bx602Pc+tfb+WJ2U8w6fnnsH2+i7rnn6fuf56hYdkfoorWj8GkJyPXHFWYGbnmiGPxIKXk+M7trH/zjZjnxLOMLRi/QD1nh2FPHQXiCwjpRorIx7G/LXPrDsoN7iId9WU/+8tLjN/8E1LFuY2eW6WJx4338A/rCL6YeYivFVVyXstWRMNh3wkp2ewumcyDooYqt5UHJj3AgvF3oBO6gGjb69OCL7i0+vW9uJ3d67MGi7Rq324ycvMYNmEi+z9ZGzbUFWV6ZhQiBarDZK9Gb9jLkFklnNp5GFvzpRFDXelZazS5eqarqD5rD9JexPizv7xEyZYnKJR11Ih8Kic/xNTrF/LB3hqefv8AO0+epSQ3lR/MsHBt5iEMx9fB0bU0Nx5hSX4uqzLSqRAWHh1+MzkjvgBF47Ht3hNVtENGjeL06dMATB1xOddP/ya5GYU0WGv468bfsenQBwAUFRVRXV0d8/1EE+n0G+cy/vKrMBiNnVrG1pFAr/jagpB0ocHRYC0vc+sOSqw9TKcjxm3XhIv2/stGcdPkIRitp5BH17Jy/x/5dcsBcj1unqipY5JIg9JZUHYJNsdg6v64Cuvq1YFA1GuNjVjjyK4Y7TvvSKTx0lmBKkJRYu0lwq3syGkz2PLeX9q1Qu2KVq9jd/1uHlz9Hapaqnkg9TwWVB9D19CWkSIlG5txEnWfObFuO8JZj4c/NDYw6dLLsJp0SNmCEOlkuLwsClpY8NLdd2NtbAiUp2SkkjO4MC6RRrN+k2/+ohJoglBi7UX8Vvb93z6Px+UMKWuvf9eeaO2elsAkioohFTx6wX3kVH8OR9fA0bXQcBhbg5FTOzLYYrqIYzlOIHhfWQMWt5FFb7/Jr+bOxYgjrBwQOq64Y1G7ljTWWKj/eiXQ7qPE2sNEGzd8afE3zuUnDiIjN49FL/wh5vXhonWdqeapb17FjZMG887BNwOTKJ6Y/QSTCif5rj1zgtsryphTZqA57QakjBzf9WECnNGLhIX0jNvbfZ8efYovz3IYereN82ZVhQi0O8vrBjJKrH3Af8+73rfjehRyh5RQUj6BknETGDp2POnZkcvpYlnaMaVN/GjtQ1RZq3hg8gMsGLcAnTiXi/fJuV+K2SajrgCXN/pYKUBO2kXtviebaVbEfrZtjeXel65o91pFfKhJEX1ArOV35rR0sgoK2b1mNdv/9XcguniFEFwxtojLxxQGRPuDt3ZQkpvKXZf+hm22l32TKKo38egljwbqFyI9qmUVIp1vr1jGf391bszyO195pN33FHOWkRoL7RWUWHuI6MvvzFxx592MrbgMr8fD6SMHqdy1kxO7d7Yr3nDRPvLuIYbmfpFrLxzF+6eWcutfbyVtZBqtB1vJcHlpNhgI77NmtM0VdkowEqU8p+OZQil5W/GE9VnPpfwcOFMC+wrlBvcgnRmT9Ho81Bw5ROXunVTu3snJvbtw2mxAqHiHjBnHxmpXwD0uLqzDOOh1GuxVnH7zNHX/qOOlm27Baow/GpyRk8vCF16I6z2psdCeRfVZNUjH4h3PmaxS3jhuZEu9FVPe65jzD9C83UrZyRLmpKSTYddhTfGyuqWFj99aE6hbBXeSFyXWfkB74jXnF/PZWQOnh+hJT93MRftyMHjPRW3dOi9/d1n5+K01Hc5gUvQtKsDUD9Dp9QwaOZpBI0cz7YabI8Q7tWUXzqM2IDIAZPDquDw9g4+URdU0SqwaJZZ4X/vxdxFR1ual27W71aHCx4DbmKq/4hdvS0p06xnruEI7KLH2MwwzZ+LWhU7md+u8GGbO7KMWKRKFEms/48eLfoJ7zkysKV4kEmuKF/ecmfx40U/6ummKbqKiwQpFEtFeNFhZVoVCIyixKhQaQYlVodAISqwKhUZQYlUoNEKnosFCiFrgWM81R6EY8JRKKQuiFXRKrAqFou9QbrBCoRGUWBUKjaDEqlBoBCVWhUIjKLEqFBpBiVWh0AhKrAqFRlBiVSg0ghKrQqER/n/9i5tZ3/4r4QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "radius2 = 10\n",
    "side2  = range(-14, 15)\n",
    "start2 = Point(0, -radius2 - 2)\n",
    "track2 = Track({Point(x, y) for x in side2 for y in side2 \n",
    "                if radius2 <= abs(Point(x, y)) <= radius2 + 3}, \n",
    "               radius=radius2, start=start2, \n",
    "               finish=[Point(0, -radius2), Point(0, -radius2 - 3)])\n",
    "\n",
    "solutions2 = search(track2)\n",
    "    \n",
    "plot(solutions2, track=track2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[6, 6, 3, 1, 1, 2, 4, 7, 4, 7, 7, 8, 9, 9, 9, 9, 5, 3, 3, 9, 3],\n",
       " [6, 6, 3, 1, 1, 2, 4, 7, 4, 7, 7, 8, 9, 9, 9, 9, 5, 3, 6, 3, 3],\n",
       " [6, 6, 3, 1, 1, 2, 4, 7, 4, 7, 7, 8, 9, 9, 9, 9, 5, 3, 3, 6, 9],\n",
       " [6, 6, 3, 1, 1, 2, 4, 7, 4, 7, 7, 8, 9, 9, 9, 9, 5, 3, 3, 6, 6],\n",
       " [6, 6, 3, 1, 1, 2, 4, 7, 4, 7, 7, 8, 9, 9, 9, 9, 5, 3, 3, 6, 3],\n",
       " [6, 3, 3, 2, 1, 7, 4, 7, 1, 7, 8, 8, 7, 9, 9, 9, 9, 3, 3, 3, 3]]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[digits_from_path(path) for path in solutions2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Additional tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tests pass'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start = track.start\n",
    "path1 = [start, Point(1, -4)] # First move\n",
    "\n",
    "assert start == Point(0, -5) == 0-5j\n",
    "assert X(start) == 0 and Y(start) == -5 \n",
    "assert velocity([start]) == 0\n",
    "assert velocity(path1) == Vector(1, 1)\n",
    "assert XY(path1) == ([0, 1], [-5, -4])\n",
    "\n",
    "assert quadrant(Point(1, -4)) == 4 == quadrant(start)\n",
    "assert quadrant(Point(1, 2))  == 1\n",
    "assert quadrant(Point(-5, 4)) == 2\n",
    "assert quadrant(Point(-1, -1))== 3\n",
    "\n",
    "assert waypoints(0, 100, 10) == [0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100]\n",
    "assert waypoints(zero, Point(10, 20), 10) == [\n",
    "    0j,1+2j,2+4j,3+6j,4+8j,5+10j,6+12j,7+14j,8+16j,9+18j,10+20j]\n",
    "\n",
    "# There are 9 moves from the start point\n",
    "assert all_moves([start]) == {\n",
    "    -1-4j, -1-5j,  -1-6j, \n",
    "     0-4j,  0-5j,   0-6j, \n",
    "     1-4j,  1-5j,   1-6j}\n",
    "\n",
    "# But 3 moves are backwards and 1 stays in the same place; those are disallowed\n",
    "assert riddler_track_moves([start]) == {0-6j, 1-6j, 1-5j, 0-4j, 1-4j}\n",
    "assert expand({(start, zero): [start]}) == {\n",
    " (0-6j, 0-1j): [0-5j, 0-6j],\n",
    " (1-6j, 1-1j): [0-5j, 1-6j],\n",
    " (1-5j, 1+0j): [0-5j, 1-5j],\n",
    " (0-4j, 0+1j): [0-5j, 0-4j],\n",
    " (1-4j, 1+1j): [0-5j, 1-4j]}\n",
    "\n",
    "for path in solutions:\n",
    "    digits = digits_from_path(path)\n",
    "    assert path   == path_from_digits(digits_from_path(path))   # Inverses\n",
    "    assert digits == digits_from_path(path_from_digits(digits)) # Inverses\n",
    "\n",
    "'tests pass'"
   ]
  }
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